Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class A {
	
	static String sol(long n) {
		Set<Long> sums = new HashSet<Long>();
		String y = "YES", no = "NO";
		
		for(long i = 1; i * (i + 1) < 2 * n; i++) {
			long triangle = i * (i + 1) / 2;
			if(2 * triangle == n) {
				return y;
			}
			if(sums.contains(n - triangle)) {
				return y;
			}
			sums.add(triangle);
		}
		return no;
	}

	public static void main(String[] args) {
		
		Scanner scn = new Scanner(System.in);
		long n = scn.nextLong();

		System.out.println(sol(n));
	}

}